Collection depots facility location problems in trees
Bibliographic record
Abstract
Abstract We consider a generalization of the median and center facility location problem called the collection depots facility location (CDFL) problem. We are given a set of client locations and a set of collection depots and we are required to find the placement for a certain number of facilities, so that the cost of dispatching a vehicle from a facility, to a client, to a collection depot, and back, is optimized for all clients. The CDFL center problem minimizes the cost of the most expensive vehicle tour among all clients, and the CDFL median problem minimizes the sum of the tour costs for all clients. We provide the first polynomial time algorithms to solve the 1 and k median problems in trees with time complexities O(n log n) and O(kn3), respectively, where n is the number of vertices in the tree. In contrast, a restricted version of the k‐median problem, where clients are given lists of allowed collection depots, is NP‐complete even for star graphs. We also give an optimal linear time algorithm to solve the discrete and continuous weighted 1‐center problem, improving on the O(n log n) result of Tamir and Halman [Discrete Optimization 2(2005), 168–184]. © 2008 Wiley Periodicals, Inc. NETWORKS, 2009
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".